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Chapter 14 “The Behavior of Gases”

Chapter 14 “The Behavior of Gases”. Section 14.1 The Properties of Gases. Compressibility. Gases can expand to fill its container, unlike solids or liquids The reverse is also true: They are easily compressed , or squeezed into a smaller volume

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Chapter 14 “The Behavior of Gases”

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  1. Chapter 14“The Behavior of Gases”

  2. Section 14.1The Properties of Gases

  3. Compressibility • Gases can expand to fill its container, unlike solids or liquids • The reverse is also true: • They are easily compressed, or squeezed into a smaller volume • Compressibility is a measure of how much the volume of matter decreases under pressure

  4. Compressibility • This is the idea behind placing “air bags” in automobiles • In an accident, the air compresses more than the steering wheel or dash when you strike it • The impact forces the gas particles closer together, because there is a lot of empty space between them

  5. Compressibility • At room temperature, the distance between particles is about 10x the diameter of the particle • Fig. 14.2, page 414 • This empty space makes gases good insulators(example: windows, coats) • How does the volume of the particles in a gas compare to the overall volume of the gas?

  6. Variables that describe a Gas • The four variables and their common units: 1. pressure (P) in kilopascals 2. volume (V) in Liters 3. temperature (T) in Kelvin 4. amount (n) in moles • The amount of gas, volume, andtemperature are factors that affect gas pressure.

  7. 1. Amount of Gas • When we inflate a balloon, we are adding gas molecules. • Increasing the number of gas particles increases the number of collisions • thus, the pressure increases • If temperature is constant, then doubling the number of particles doubles the pressure

  8. Pressure and the number of molecules are directly related • More molecules means more collisions, and… • Fewer molecules means fewer collisions. • Gases naturally move from areas of high pressure to low pressure, because there is empty space to move into – a spray can is example.

  9. Common use? • A practical application is Aerosol (spray) cans • gas moves from higher pressure to lower pressure • a propellant forces the product out • whipped cream, hair spray, paint • Fig. 14.5, page 416 • Is the can really ever “empty”?

  10. 2. Volume of Gas • In a smaller container, the molecules have less room to move. • The particles hit the sides of the container more often. • As volume decreases, pressure increases. (think of a syringe) • Thus, volume and pressure are inversely related to each other

  11. 3. Temperature of Gas • Raising the temperature of a gas increases the pressure, if the volume is held constant. (Temp. and Pres. are directly related) • The molecules hit the walls harder, and more frequently! • Fig. 14.7, page 417 • Should you throw an aerosol can into a fire? What could happen? • When should your automobile tire pressure be checked?

  12. Section 14.2The Gas Laws

  13. The Gas Laws are mathematical • The gas laws will describe HOW gases behave. • Gas behavior can be predicted by the theory. • The amount of change can be calculated with mathematical equations. • You need to know both of these: the theory, and the math

  14. Robert Boyle(1627-1691) • Boyle was born into an aristocratic Irish family • Became interested in medicine and the new science of Galileo and studied chemistry.  • A founder and an influential fellow of the Royal Society of London • Wrote extensively on science, philosophy, and theology.

  15. #1. Boyle’s Law - 1662 Gas pressure is inversely proportional to the volume, when temperature is held constant. • Pressure x Volume = a constant • Equation: P1V1 = P2V2 (T = constant)

  16. Graph of Boyle’s Law – page 418 Boyle’s Law says the pressure is inverse to the volume. Note that when the volume goes up, the pressure goes down

  17. - Page 419

  18. Boyle’s Law Practice Ammonia gas occupies a volume of 450. mL at 720. mm Hg. What volume will it occupy at standard pressure? V2 = 426 mL A 3.2-L sample of gas has a pressure of 102 kPa. If the volume is reduced to 0.65 L, what pressure will the gas exert? P2 = 502 kPa

  19. Jacques Charles (1746-1823) • French Physicist • Part of a scientific balloon flight on Dec. 1, 1783 – was one of three passengers in the second balloon ascension that carried humans • This is how his interest in gases started • It was a hydrogen filled balloon – good thing they were careful!

  20. #2. Charles’s Law - 1787 • The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant. • This extrapolates to zero volume at a temperature of zero Kelvin.

  21. Converting Celsius to Kelvin • Gas law problems involving temperature will always require that the temperature be in Kelvin. (Remember that no degree sign is shown with the kelvin scale.) • Reason? There will never be a zero volume, since we have never reached absolute zero. Kelvin = C + 273 °C = Kelvin - 273 and

  22. - Page 421

  23. Charles's Law Practice Helium occupies 3.8 L at -45°C. What volume will it occupy at 45°C? V2 = 5.3 L At 27°C, fluorine occupies a volume of 0.500 dm3. To what temperature in degrees Celsius should it be lowered to bring the volume to 200. mL? T2 = -153°C (120 K)

  24. Joseph Louis Gay-Lussac (1778 – 1850) • French chemist and physicist • Known for his studies on the physical properties of gases. • In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes.

  25. #3. Gay-Lussac’s Law - 1802 • The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant. • How does a pressure cooker affect the time needed to cook food? (Note page 422) • Sample Problem 14.3, page 423

  26. Gay-Lussac’s Practice Problems A gas at STP is cooled to -185°C. What pressure in kPa will it have at this temperature (volume remains constant)? P2 = 0.32 atm Chlorine gas has a pressure of 1.05 kPa at 25°C. What pressure will it exert at 75°C? P2 = 1.23 atm

  27. #4. The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas. Sample Problem 14.4, page 424

  28. The combined gas law contains all the other gas laws! • If the temperature remains constant... P1 V1 P2 x V2 x = T1 T2 Boyle’s Law

  29. The combined gas law contains all the other gas laws! • If the pressure remains constant... P1 V1 P2 x V2 x = T1 T2 Charles’s Law

  30. The combined gas law contains all the other gas laws! • If the volume remains constant... P1 V1 P2 x V2 x = T1 T2 Gay-Lussac’s Law

  31. Combined Gas Law Pracitce A gas occupies 256 mL at 720 kPa and 25°C. What will its volume be at STP? V2 = 220 mL A gas occupies 1.5 L at 850 kPa and 15°C. At what pressure will this gas occupy 2.5 L at 30.0°C? P2 = 540 kPa A gas occupies 125 mL at 125 kPa. After being heated to 75°C and depressurized to 100.0 kPa, it occupies 0.100 L. What was the original temperature of the gas? T1 = 544 K (271°C)

  32. Section 14.3Ideal Gases

  33. 5. The Ideal Gas Law #1 • Equation: P x V = n x R x T • Pressure times Volume equals the number of moles (n) times the Ideal Gas Constant (R) times the Temperature in Kelvin. • R = 8.31 (L x kPa) / (mol x K) • The other units must match the value of the constant, in order to cancel out. • The value of R could change, if other units of measurement are used for the other values (namely pressure changes)

  34. The Ideal Gas Law • We now have a new way to count moles (the amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions: P x V R x T n =

  35. Ideal Gases • We are going to assume the gases behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure • An ideal gas does not really exist, but it makes the math easier and is a close approximation. • Particles have no volume? Wrong! • No attractive forces? Wrong!

  36. Ideal Gases • There are no gases for which this is true (acting “ideal”); however, • Real gases behave this way at a) high temperature, and b) low pressure. • Because at these conditions, a gas will stay a gas! • Sample Problem 14.5, page 427

  37. #6. Ideal Gas Law 2 • P x V = m x R x T M • Allows LOTS of calculations, and some new items are: • m = mass, in grams • M = molar mass, in g/mol • Molar mass = m R T P V

  38. Density • Density is mass divided by volume m V so, m M P V R T D = D = =

  39. Ideal Gas Law Practice

  40. P1xV1 P2xV2 T1 T2 = (101.6 kPa)x(200 dm3) (98.6 kPa)x(150 dm3) 290 K T2 = Gas Review Problem #1 1)  A quantity of gas has a volume of 200 dm3 at 17oC and 106.6 kPa.  To what temperature (oC) must the gas be cooled for its volume to be reduced to 150 dm3 at a pressure of 98.6 kPa? Write given information: V1  =                                   V2  =  T1  =          T2  =  P1  =                              P2  =  200 dm3 150 dm3 17 oC +  273   =  290 K _______ 106.6 kPa 98.6 kPa Write equation:   Substitute into equation:        Solve for T2:   Recall: oC  +  273  =  K Therefore:  Temperature  =  -71oC T2  =  201 K

  41. P1xV1 P2xV2 T1 T2 P1 P2 T1 T2 = = 98.6 kPa P2 295 K 265 K = (295 K) (295 K) (98.6 kPa)(265) (295) P2 = Gas Review Problem #2 2)  A quantity of gas exerts a pressure of  98.6 kPa at a temperature of 22oC.  If the volume remains unchanged, what pressure will it exert at -8oC? Write given information: V1  =                                V2  =  T1  =         T2  =  P1  =                                P2  =  constant  constant 22 oC +  273   =  295 K -8 oC +  273   =  265 K 98.6 kPa _________ Write equation:   Volume is constant...cancel it out from equation:  Substitute into equation: Solve for P2:   To solve, cross multiply and divide: (P2)(295 K) (98.6 kPa)(265 K) = P2  =  88.6 kPa

  42. = mass volume P1xV1P2xV2 Density = (98.7 kPa)x(3.34 L)(101.3 kPa)x(V2) mass 2.85 L = T1 T2 3.17 g/cm3 = 310 K 273K (98.7 kPa)(3.34 dm3) PV n n = = [8.314 (kPa)(dm3)/(mol)(K)](310 K) RT Gas Review Problem #3 What is the mass of 3.34 dm3 sample of chlorine gas if the volume was determined at 37oC and 98.7 kPa?  The density of chlorine gas at STP is 3.17 g/dm3. Write given information: V1  =                                       V2  =  T1  =          T2  =   P1  =                                  P2  =  R  =                    Density  =  n  =  Cl2  =  Two approaches to solve this problem. METHOD 1:  Combined Gas Law & Density Write equation:   Substitute into equation:    Solve for V2: Density  =  3.17 g/dm3 @ STP Recall:    Substitute into equation:    Solve for mass:  __________ 3.34 L 273  K 37 oC +  273   =  310 K 98.7 kPa 101.3 kPa 8.314 kPa L / mol K 3.17 g/dm3 ___________ 71 g/mol 2.85 L V2  =  2.85 L @ STP PV = nRT mass  =  9.1 g chlorine gas

  43. METHOD 2:  Ideal Gas Law Write equation:   Solve for moles:    Substitute into equation:    Solve for mole:  n  =  0.128 mol Cl2 Recall molar mass of diatomic chlorine is 71 g/mol Calculate mass of chlorine:  x g Cl2  =  0.128 mol Cl2   =  9.1 g Cl2

  44. 1 mol FeS 1 mol H2S 879 g FeS 1 mol FeS (L)(Kpa) (mol)(K) (95.1 kPa)(V) = 1.5 mol H2S 8.314 (303 K) Gas Review Problem #6 Iron (II) sulfide reacts with hydrochloric acid as follows: FeS(s)  +  2 HCl(aq)    FeCl2(aq)  +  H2S(g) What volume of H2S, measured at 30oC and 95.1 kPa, will be produced when 132 g of FeS reacts? Calculate number of moles of H2S... x mole H2S  =  132 g FeS  Write given information: P  =  n  =  R  =  T  =  Equation: Substitute into Equation:  Solve equation for Volume:  132 g X L = 1.50 mol H2S 95.1 kPa 1.5 mole H2S 8.314 L kPa/mol K 30oC +  273  =  303 K PV  =  nRT V  =  39.7 L

  45. Gas Review Problem #6 7)  What is the density of nitrogen gas at STP (in g/dm3 and kg/m3)? Write given information: 1 mole N2  =  28 g N2  =  22.4 dm3 @ STP Write equation: Substitute into equation:  Solve for Density:   Density  =  1.35 g/dm3 Recall:  1000 g  =  1 kg     &     1 m3  =  1000 dm3 Convert m3 to dm3:         x dm3  =  1m3                      =  1000 dm3 Convert: Solve: 1.35 kg/m3

  46. Real Gases and Ideal Gases

  47. Ideal Gases don’t exist, because: • Molecules do take up space • There are attractive forces between particles - otherwise there would be no liquids formed

  48. Real Gases behave like Ideal Gases... • When the molecules are far apart. • The molecules do not take up as big a percentage of the space • We can ignore the particle volume. • This is at low pressure

  49. Real Gases behave like Ideal Gases… • When molecules are moving fast • This is at high temperature • Collisions are harder and faster. • Molecules are not next to each other very long. • Attractive forces can’t play a role.

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